Roberto hit .314/.455/.471 with 27 walks and 26 runs in 28 games in '82. He debuted for the Italian national team at age 19 in the 1982 Amateur World Series. In the 1983 campaign, the Bologna slugger batted .482/.550/.819 with 13 doubles, 15 walks, 28 runs and 36 RBI in 18 games in the Serie A Girone B, then hit .347/.445/.627 with 11 home runs, 45 runs and 44 RBI in 39 games in the Poule Scudetto. He helped Italy win a Gold Medal at the 1983 European Championship, being named the best hitter after batting .487 with 3 home runs and 15 RBI in their 9 games.

Bianchi's batting line in 1984 read .408/.538/.887 with 18 walks, 9 home runs, 29 runs and 28 RBI in 20 games in the Serie Nazionale Lega Est, then .430/.589/.793 with 50 walks, 45 runs and 45 RBI in 41 contests in the Poule Scudetto. He was .006 behind batting champion Craig Stimac, a former major leaguer. He helped Bologna win the title, the only pennant they took during his gloried seasons with them. Roberto played for Italy in the 1984 Olympics. In the 1984 Amateur World Series, he hit .500/.546/1.025 with 6 HR, 12 R and 20 RBI in 10 games, primarily at catcher. He led the Series in average by .025 over Víctor Mesa and was the lone non-Cuban in the top five. He tied Luis Casanova and Pedro Jose Rodriguez Sr. for the home run lead and tied Casanova for 3rd with 20 hits, trailing only Mesa and Alfonso Urquiola. He also led the event in RBI, 4 ahead of runners-up Barry Bonds and Lourdes Gourriel. Jim Dietz listed him as a pro prospect that year.

Bianchi put together a strong season in 1985, hitting .392/.542/.804 with 76 walks, 26 home runs, 106 runs and 102 RBI in 67 games. He shattered Stimac's RBI record of 74; no one else has even reached triple digits in Italian history. Roberto helped Italy win a Silver Medal at the 1985 European Championship.

Roberto kept on slugging in '86, producing at a .466/.560/.960 clip with 51 walks, 23 home runs, 74 runs and 84 RBI in 48 games. He won his first batting title and led in RBI for the third time. He was one home run shy of a Triple Crown, trailing Dave Malpeso. He was named the All-Star catcher at the 1986 Amateur World Series after hitting .414 with 5 home runs and a tourney-best 18 runs. He was one homer behind tourney leader Casanova of Cuba.

In 1987, Bianchi won his first Triple Crown, hitting .474/.588/1.051 with 41 walks, 16 steals in 19 tries, 27 home runs, 70 runs and 72 RBI in just 41 games. He was just the third Triple Crown winner in Italian baseball history following Roberto Gandini (1962) and Castelli (1974). He played in the 1987 Intercontinental Cup and 1987 European Championship (in which Italy won a Silver Medal).

Bianchi batted .351/.528/.743 for Bologna in 1988 with 28 walks, 27 runs and 25 RBI in 22 games. In the 1988 Baseball World Cup, Roberto hit only .235/.341/.265 in a disappointing showing as Italy's left fielder. Roberto hit .387/.526/.824 in 1989 with 45 walks, 15 home runs, 46 runs and 53 RBI in 42 games. He won his second home run crown and 5th RBI title that year. He was 39 points behind batting champion Giuseppe Carelli. He played in the 1989 Intercontinental Cup and 1989 European Championship (as Italy took Gold).

Roberto's pace did not slacken as he ended his first decade. He hit .368/.519/.741 for Milano in 1990 with 61 walks, 85 runs, 18 home runs and 75 RBI in 62 games. He was two home runs shy of the league lead. In the 1990 Baseball World Cup, the veteran hit .417/.563/.667 with 7 RBI in 7 games while alternating between catcher and DH, leading Italy's offense once more in a major tournament.

In 1991, the Milan native hit .460/.580/.921 for his hometown club with 38 walks, 16 homers, 45 runs and 55 RBI in 36 games. He became the first two-time Triple Crown winner in Italian history. It would be 19 years before another player (Carlos Duran would win a Tripla Corona in Italy. He then batted .414/.457/.724 for Italy in the 1991 Intercontinental Cup, leading Italy's hitters again. In the 1991 European Championship, he was named best hitter and Italy took home the title. It would be his last appearance in the European Championships; with 3 Gold Medals, he was one of the top medalists in Italian history.

Bianchi batted .394/.492/.827 with 13 homers, 38 runs and 43 RBI in 29 games in 1992. He was one home run behind leader David Sheldon. In the 1992 Olympics, the 29-year-old hit .200/.500/.267 as Italy's main DH. He tied Jason Giambi for the most walks (9) in the Summer Games that year and only had two fewer walks than the entire Spanish team; this despite sitting out two of Italy's 8 games.

In 1993, Roberto's batting line was .448/.523/.784 for his new Parma club. He had 40 runs and 51 RBI in 33 contests for his 7th and last time leading the Serie A1 in RBI. He was just 2 for 17 as Italy's first baseman in the 1993 Intercontinental Cup. It was his last major tournament with the Italian national team, having played 150 games for them on the international stage. Through 2009, only longtime Azzurri teammate Ruggero Bagialemani had played more games for Italy.

Bianchi batted .353/.480/.660 for Parma in '94 with 53 runs and 51 RBI in 46 games. He was 10 RBI behind leader Brad Komminsk. He won his second pennant that year. In 1995, he hit .422/.515/.797 with Parma with 23 doubles, 15 home runs, 55 runs and 65 RBI in 54 games. He was .005 shy of Jessie Reid for the batting title, 4 home runs behind leader Reid and two RBI behind leader Francesco Casolari, nearly taking home another Triple Crown in his 15th year. He helped Parma win another title.

The old-timer produced at a .356/.502/.684 rate in 1996 with 61 runs and 52 RBI in 50 games. That year, he told the Fort Lauderdale Sun-Sentinel that "I love baseball more than I love myself." Despite his success on the field, he could walk down an Italian street without drawing notice due to the low profile of the game in his nation.

At age 34, Bianchi hit .384/.506/.664 for Modena with 49 walks, 48 runs and 64 RBI in 53 games. In '98, he batted .355/.449/.633 with Rimini, scoring 43 and driving in 57 in 44 games. He was only 7 RBI behind leader Massimo Fochi. He was 7 for 15 in the finals but Rimini failed to take the title. He wrapped up his playing career in 1999, hitting .371/.491/.484 with just one home run in 28 games.

Overall, Bianchi had batted .384/.508/.730 in 949 games in Italy. He had 1,106 runs, 270 doubles, 288 home runs, 1,170 RBI, 843 walks and 134 steals in 174 tries. Through 2008, he is among Italy's all-time leaders in homers (1st, 68 over runner-up Carelli), hits (1,307, 3rd behind Roberto De Franceschi and Bagialemani), RBI (1st by 246 over Carelli), runs (1st by 39 over De Franceschi) and average (4th behind Castelli, Stimac and Jesse Baez).